On the leading and penultimate leading coefficients for NRS(2) applied to a cubic polynomial
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917332917420032 |
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| author | DeFranco, Mario |
| author_facet | DeFranco, Mario |
| contents | We prove that the leading and penultimate leading coefficients in $u_3$ of the ``error" terms of NRS(2) applied to a cubic polynomial $f(z) =\sum_{i=0}^3 a_i z^i=\prod_{i=1}^3 (1-u_iz)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient polynomials in $u_1$ and $u_2$. Our proof for the leading coefficients simplifies that of \cite{DeFranco} and extends to the penultimate leading coefficients as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10728 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the leading and penultimate leading coefficients for NRS(2) applied to a cubic polynomial DeFranco, Mario Combinatorics We prove that the leading and penultimate leading coefficients in $u_3$ of the ``error" terms of NRS(2) applied to a cubic polynomial $f(z) =\sum_{i=0}^3 a_i z^i=\prod_{i=1}^3 (1-u_iz)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient polynomials in $u_1$ and $u_2$. Our proof for the leading coefficients simplifies that of \cite{DeFranco} and extends to the penultimate leading coefficients as well. |
| title | On the leading and penultimate leading coefficients for NRS(2) applied to a cubic polynomial |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.10728 |